Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2816 |
528 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,b^2=e,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35305040, #35305042, #35305057, … |
| maximal normal subgroup of | #35305040, #35305042, #35305057, … |
| maximal quotient of | #35335047, #35335073, #35335085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12537);